2n=48-n^2

Solution for 2n=48-n^2 equation:

Simplifying
2n = 48 + -1n2

Solving
2n = 48 + -1n2

Solving for variable 'n'.

Reorder the terms:
-48 + 2n + n2 = 48 + -1n2 + -48 + n2

Reorder the terms:
-48 + 2n + n2 = 48 + -48 + -1n2 + n2

Combine like terms: 48 + -48 = 0
-48 + 2n + n2 = 0 + -1n2 + n2
-48 + 2n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-48 + 2n + n2 = 0

Factor a trinomial.
(-8 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-8, 6}